Sequence of Powers of Reciprocals is Null Sequence/Corollary
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Corollary to Sequence of Powers of Reciprocals is Null Sequence
Let $\sequence {x_n}$ be the sequence in $\R$ defined as:
- $x_n = \dfrac 1 n$
Then $\sequence {x_n}$ is a null sequence.
Proof
$n = n^1$ from the definition of power.
As $1 \in \Q_{>0}$ the result follows from Sequence of Powers of Reciprocals is Null Sequence.
$\blacksquare$